A244874 Number of magic labelings with magic sum n of 6th graph shown in link.

1, 17, 137, 707, 2709, 8417, 22408, 53008, 114251, 228431, 429325, 766167, 1308451, 2151643, 3423880, 5293736, 7979133, 11757477, 16977097, 24070067, 33566489, 46110317, 62476800, 83591624, 110551831, 144648595, 187391933, 240537431, 306115063, 386460183, 484246768

Offset: 0

Author

N. J. A. Sloane, Jul 08 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Graphs for A244869-A244876.
• R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
• Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1).

Crossrefs

Cf. A244869, A244870, A244871, A244872, A244873, A244875, A244876.

Programs

Mathematica

LinearRecurrence[{7,-20,28,-14,-14,28,-20,7,-1},{1,17,137,707,2709,8417,22408,53008,114251},40] (* Harvey P. Dale, Jun 30 2022 *)

PARI

Vec((1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)) + O(x^40)) \\ Colin Barker, Jan 11 2017

Formula

G.f.: (1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)).

a(n) = (-315*(-129+(-1)^n) + 138528*n + 202104*n^2 + 171248*n^3 + 93030*n^4 + 32312*n^5 + 6636*n^6 + 632*n^7) / 40320. - Colin Barker, Jan 11 2017